# Nature (1876) Algorithm for Calculating the Date of
Easter in the Gregorian Calendar

*Originally published 1996 December by
M.J. Montes.*

*This page was last updated 2001 July 31 by Marcos J. Montes.*

The actual origin of this algorithm appears to be by an anonymous
correspondent from New York to Nature in 1876 (Thanks
Denis!). Samuel Butcher, Bishop of Meath, showed that this algorithm
followed from Delambre's analytical solutions, and produces the date of
Easter for all years. You can see the algorithm, as well as version for
Orthodox Easter at another Easter
Date site.
This algorithm appears in Practical Astronomy With Your Calculator, 2nd
Edition by Peter Duffett-Smith, and he obtained this algorithm
from Butcher's Ecclesiastical Calendar,
published in 1876. This algorithm has also been published in the 1922
book General Astronomy by Spencer Jones; in The Journal
of the British Astronomical Association (Vol.88, page 91, December
1977); and in Astronomical Algorithms (1991) by Jean Meeus.

This algorithm holds for any year in the Gregorian Calendar,
which (of course) means years including and after 1583.

In the text below, **/** represents an integer division
neglecting the
remainder, while **%** is division keeping only the
remainder. So 30/7=4 , and 30%7=2 .

a=year%19
b=year/100
c=year%100
d=b/4
e=b%4
f=(b+8)/25
g=(b-f+1)/3
h=(19*a+b-d-g+15)%30
i=c/4
k=c%4
l=(32+2*e+2*i-h-k)%7
m=(a+11*h+22*l)/451
Easter Month =(h+l-7*m+114)/31 [3=March, 4=April]
p=(h+l-7*m+114)%31
Easter Date=p+1 (date in Easter Month)

### References

- Nature, 1876 April 20, vol. 13, p. 487.
- Dennis Roegel

### Links

Oudin's Algorithm for the calculation of the
date of Easter.

Carter's Algorithm for the calculation of the date
of Easter.

Gauss' Algorithm for the calculation of the
date of the Orthodox Easter.

Calculation of the Ecclesiastical Calendar

Last updated 2001 July 31.
Marcos J. Montes

mmontes@no.spam.smart.net